English
Related papers

Related papers: The Elliptic Gaudin Model: a Numerical Study

200 papers

The paper discusses the transformation of decorated Ising models into an effective \textit{undecorated} spin models, using the most general Hamiltonian for interacting Ising models including a long range and high order interactions. The…

Mathematical Physics · Physics 2011-03-02 Onofre Rojas , J. S. Valverde , S. M. de Souza

We propose a one-dimensional model of spinor bosons with SU(2) symmetry and a two-body finite range Gaussian interaction potential. We show that the model is exactly solvable when the width of the interaction potential is much smaller…

Statistical Mechanics · Physics 2012-01-25 J. Y. Lee , X. W. Guan , A. del Campo , M. T. Batchelor

We introduce novel polynomial deformations of the Lie algebra $sl(2)$. We construct their finite-dimensional irreducible representations and the corresponding differential operator realizations. We apply our results to a class of spin…

Mathematical Physics · Physics 2025-09-16 Siyu Li , Ian Marquette , Yao-Zhong Zhang

We prove, using the coordinate Bethe ansatz, the exact solvability of a model of three particles whose point-like interactions are determined by the root system of g_2. The statistics of the wavefunction are left unspecified. Using the…

Mathematical Physics · Physics 2007-05-23 N. Crampe , C. A. S. Young

We present an electronic model with long range interactions. Through the quantum inverse scattering method, integrability of the model is established using a one-parameter family of typical irreducible representations of gl(2|1). The…

Statistical Mechanics · Physics 2007-05-23 K. E. Hibberd , J. R. Links

We consider the isotropic spin$-\frac{1}{2}$ Heisenberg chain with the most general integrable boundaries. The scalar product between the on-shell Bethe vector and its off-shell dual, obtained by means of the modified algebraic Bethe…

Mathematical Physics · Physics 2016-03-23 S. Belliard , R. A. Pimenta

The Lieb-Liniger model describes one-dimensional bosons with contact interactions. This many-body system admits an exact solution in terms of the Bethe ansatz. Some of the exact and perturbative results for this model are reviewed.…

Quantum Gases · Physics 2026-04-29 Zoran Ristivojevic

The quasiclassical asymptotics of the Knizhnik-Zamolodchikov system is studied. Solutions to this system in this limit are related naturally to Bethe vectors in the Gaudin model of spin chains.

High Energy Physics - Theory · Physics 2008-02-03 Nicolai Reshetikhin , Alexander Varchenko

We calculate the correlation functions of strings of spin operators for integrable quantum circuits exactly. These observables can be used for calibration of quantum simulation platforms. We use algebraic Bethe Ansatz, in combination with…

Quantum Physics · Physics 2025-07-02 Arthur Hutsalyuk , Yunfeng Jiang , Balazs Pozsgay , Hefeng Xu , Yang Zhang

Modeling complex systems, like neural networks, simple liquids or flocks of birds, often works in reverse to textbook approaches: given data for which averages and correlations are known, we try to find the parameters of a given model…

Statistical Mechanics · Physics 2023-04-25 Tobias Kühn , Frédéric van Wijland

We apply the thermodynamic Bethe Ansatz to investigate the high energy behaviour of a class of scattering matrices which have recently been proposed to describe the Homogeneous sine-Gordon models related to simply laced Lie algebras. A…

High Energy Physics - Theory · Physics 2014-11-18 O. A. Castro-Alvaredo , A. Fring , C. Korff , J. L. Miramontes

We introduce the notion of a classical dihedral affine Gaudin model, associated with an untwisted affine Kac-Moody algebra $\widetilde{\mathfrak{g}}$ equipped with an action of the dihedral group $D_{2T}$, $T \geq 1$ through (anti-)linear…

High Energy Physics - Theory · Physics 2019-03-04 Benoit Vicedo

An exactly solvable model describing the dilute spin-3/2 fermion gas in one-dimensional optical trap is proposed. The diagonalization of the model Hamiltonian is derived by means of the Bethe ansatz method. Exotic spin excitations such as…

Strongly Correlated Electrons · Physics 2009-02-18 Yuzhu Jiang , Junpeng Cao , Yupeng Wang

We formulate $Q$-systems for the closed XXZ, open XXX and open quantum-group-invariant XXZ quantum spin chains. Polynomial solutions of these $Q$-systems can be found efficiently, which in turn lead directly to the admissible solutions of…

High Energy Physics - Theory · Physics 2021-05-19 Zoltán Bajnok , Etienne Granet , Jesper Lykke Jacobsen , Rafael I. Nepomechie

We study the scalar products between Bethe states in the XXZ spin chain with anisotropy $|\Delta|>1$ in the semi-classical limit where the length of the spin chain and the number of magnons tend to infinity with their ratio kept finite and…

High Energy Physics - Theory · Physics 2017-04-05 Yunfeng Jiang , Joren Brunekreef

We present a generalization of the master solution to the quantum Yang-Baxter equation (obtained recently in arXiv:1006.0651) to the case of multi-component continuous spin variables taking values on a circle. The Boltzmann weights are…

Mathematical Physics · Physics 2015-05-28 Vladimir V. Bazhanov , Sergey M. Sergeev

In this article we study the thermodynamic limit of the form factors of the XXX Heisenberg spin chain using the algebraic Bethe ansatz approach. Our main goal is to express the form factors for the low-lying excited states as determinants…

Mathematical Physics · Physics 2021-12-28 Nikolai Kitanine , Giridhar Kulkarni

The procedure for obtaining integrable open spin chain Hamiltonians via reflection matrices is explicitly carried out for some three-state vertex models. We have considered the 19-vertex models of Zamolodchikov-Fateev and Izergin-Korepin,…

Exactly Solvable and Integrable Systems · Physics 2014-11-18 E. C. Fireman , A. Lima-Santos , W. Utiel

We construct symmetric and exterior powers of the vector representation of the elliptic quantum groups $E_{\tau,\eta}(gl_N)$. The corresponding transfer matrices give rise to various integrable difference equations which could be solved in…

q-alg · Mathematics 2009-10-30 Giovanni Felder , Alexander Varchenko

An anisotropic integrable spin chain, consisting of spins $s=1$ and $s=\frac{1}{2}$, is investigated \cite{devega}. It is characterized by two real parameters $\bar{c}$ and $\tilde{c}$, the coupling constants of the spin interactions. For…

High Energy Physics - Theory · Physics 2014-11-18 St. Meissner , B. -D. Doerfel